Couple of new thoughts.
Is this your first time abroad or in England?
Indeed everything is more expensive there than here but you must remember that your per diem expenses run regardless of what you do so while you may find a place in East Anglia where you can shoot at half the price than you can in London it makes no sense because your daily meter is running anyway.
Don't fret the expense - your trip will be more expensive than you planned but don't let it ruin your fun - just enjoy.
Contact the shooting grounds via e-mail before you leave and make firm appointments. Get directions from where you're staying. If you need to rent a car from London you will find it very expensive and that alone may make the whole day's shooting prohibitive. Make sure you check it out beforehand.
Keep us posted.